How do I calculate the electric potential

How do I calculate the electric potential "V" of a point charge "q" at radius "r" if I am told that the electrical potential is zero at a distance "d" other than infinity? I believe that there is some arbitrary constant that must be found but I don't know if, where, or how that fits in.

The V=0 at infinity because as r goes to infinity, the function becomes infinitely small.

But what if V=0 at 1meter? Then how would I find V at .5 meters? for some reason the equation V=K(q/r) doesn't work by itself in this case. The only way I can reconcile this is if there is some other part to the equation that we leave out because V=0 is usually at infinity. Any ideas?!

The V=0 at infinity because as r goes to infinity, the function becomes infinitely small.

But what if V=0 at 1meter? Then how would I find V at .5 meters? for some reason the equation V=K(q/r) doesn't work by itself in this case. The only way I can reconcile this is if there is some other part to the equation that we leave out because V=0 is usually at infinity. Any ideas?!

Is this a book question or are you having a problem with a concept? Where did you get V = 0 at 1, at r =1 ? Doesn't V = 0 at r =1 a contradiction if the equation is Kq/r? wouldn't V = kq at 1?

Exactly my problem. My professor assigned a few problems where V=0 at different distances (not infinity). Supposedly it doesn't matter where you set the zero of electric potential (just like it really doesn't matter where you choose the zero of gravitational potential), I just can't figure out how the equation should be set up.

This is how you find teh potential due to a uniformaly charged sphere, or simply a charge :

DV=change in V= potential difference=V2-V1=(Kq)/r2 - (Kq)/r1
= (Kq)[1/r2 - 1/r1]
at r1= infinity , V1= 0 Which is how you get a voltage value at a distance outside a charge, you assume r1 is infinate distance. If you really say your teacher said you can get a zero voltage. My oh my